LIFTING OF CHARACTERS AND FUNCTIONS ON METAPLECTIC GROUPS
LIFTING OF CHARACTERS AND FUNCTIONS ON METAPLECTIC GROUPS
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Date
2004-11-23
Authors
Trehan, Amit
Advisor
ADAMS, JEFFREY D
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Abstract
We study the lifting of representations between the N-fold
metaplectic covers of SL(n, F) where n|N
and PGL(n, F), F a local field, and obtain a formula relating irreducible characters
of PGL(n, F) and SL~(n, F) (the covers of
SL(n, F)). This is achieved by generalizing the approach of Adams [1].
In the second part of the thesis we study the lifting of functions
between SL~(n, F) and PGL(n, F). Using orbital
integrals we obtain the formula for the lifting of characters
as a dual to the lifting of functions. This is based on the
methods of Flicker and Kazhdan [7].
Finally we use our methods of lifting of orbital integrals
to provide alternate proof of a well-known
fact about p-adic fields (under certain restrictions). We show
that for a Galois extension E/F, F*/N(E*) isomorphic
Gal(E/F)ab where Gal(E/F) is the Galois group of
E over F and Gal(E/F)ab denotes its abelianization
and N: E* to F* is the norm map.